All-to-all Element wise l2 distance of vector

Hi all,

I want to calculate the l2 distance among all elements of two vector. naive version code is:

import torch
n = 4
d = 2
A = torch.randn(n,d)
B = torch.randn(n,d)
C = torch.zeros(n,n)

for i in range(n):
    for j in range(n):
        C[i][j] = torch.sum(torch.sqrt((A[i] - B[j])*(A[i]-B[j])))

I want to ask is there any easier way to do this calculation at PyTorch?
Thanks!
Jun

Not answeirng your quesiton, but shouldnt your sum be inside your sqrt?

As far as answering your question, isnt it just approximately the Grammian? so you can do something like:

torch.sqrt(a @ b.transpose(0,1))
1 Like

Oh, yeah. It should be inside the sqrt

Well, Thanks a lot, Is @ operator could be used in Variable and do autograd?
I want to implement my custom loss function here.

Looks like @ works ok on Variables:

In [3]: a = torch.autograd.Variable(torch.rand(3,4), requires_grad=True)

In [4]: b = torch.autograd.Variable(torch.rand(4,2), requires_grad=True)

In [5]: c = a @ b

In [6]: c
Out[6]: 
Variable containing:
 0.9375  0.5729
 1.3275  0.4193
 0.2320  0.1663
[torch.FloatTensor of size 3x2]

Cool, but it’s only the gram matrix, and I want to calculate the Euclidean Distance Matrix here (sorry, I did not explain it well before). Is there any better way?

How is this?

TwoAB = 2 * A @ B.transpose(0,1)
print(torch.sqrt(torch.sum(A * A, 1).expand_as(TwoAB) + torch.sum(B * B, 1).transpose(0,1).expand_as(TwoAB) - TwoAB))